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Market Microstructure: Confronting Many Viewpoints by Thierry Foucault, Mathieu Rosenbaum, Charles-Albert Lehalle, Frédéric Abergel, Jean-Philippe Bouchaud

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7

Collective Portfolio Optimization in Brokerage Data: The Role of Transaction Cost Structure

Damien Challet and David Morton de Lachapelle

7.1 INTRODUCTION

Regarding financial market behavior as a result of the interaction between many traders, i.e., as collective phenomena, opens the way to applying concepts and tools of statistical physics. In the last few decades, the latter has developed a powerful mathematical machinery that is able to solve the macroscopic dynamics resulting from the nonlinear microscopic interaction of fully heterogeneous adaptive complex agents, no less. One usually starts from known microscopic behavior and interaction and then study and possibly solve the resulting collective dynamics. In the case of financial markets, the lack of knowledge about the agents themselves hinders progress in this field. On the one hand, experimental psychology and behavioral finance put forward a picture of trader minds and actions that does not resemble many rational agents. On the other hand, the actual behavior of traders is seldom studied. Thus, one attempts to reverse engineer markets with agent-based models, trying painstakingly to guess what microscopic mechanism is necessary to reproduce a set of macroscopic stylized facts one observed in available data.

There has been some notable progress so far from statistical physicists. A quite important one is about volatility clustering. In game theory, giving the players the ability not to take part in a given game gives ...

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